🗜️ Dimensionality Reduction

CSharpNumerics includes unsupervised dimensionality reduction as an optional preprocessing step in both supervised and clustering pipelines. Reducers implement IDimensionalityReducer and slot into the pipeline between feature selection and scaling.

using CSharpNumerics.ML;

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📋 Pipeline Order

Pipeline	Order
Supervised	Selector → Reducer → Scaler → Model
Clustering	Reducer → Scaler → Model

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🔵 Algorithms

Principal Component Analysis (PCA)

Class: PCA

Projects data onto the top eigenvectors of the covariance matrix. Eigenpairs are computed with EigenDecomposition — direct and deterministic. When there are fewer samples than features (n < d) it works on the n × n Gram matrix (dual PCA) instead of the d × d covariance matrix.

Hyperparameters:

• NComponents — number of output dimensions

MaxIterations, Tolerance and Seed no longer affect the result (since v4.3). They are retained so existing calls and grid-search parameter dictionaries keep working.

Exposes after fit: Components, ExplainedVariance, ExplainedVarianceRatio, Mean

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🔬 Clustering Pipeline Integration

var experiment = ClusteringExperiment
    .For(X)
    .WithAlgorithm(new KMeans())
    .TryClusterCounts(2, 8)
    .WithEvaluator(new SilhouetteEvaluator())
    .WithReducer(new PCA { NComponents = 5 })
    .WithScaler(new StandardScaler())
    .Run();

Console.WriteLine(experiment.BestClusterCount);

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🔲 Clustering Grid Integration

var experiment = ClusteringExperiment
    .For(X)
    .WithGrid(new ClusteringGrid()
        .AddModel<KMeans>(g => g
            .Add("K", 2, 3, 4, 5)
            .AddReducer<PCA>(r => r.Add("NComponents", 2, 5, 10))
            .AddScaler<StandardScaler>(s => { })))
    .WithEvaluator(new SilhouetteEvaluator())
    .Run();

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⚡ Supervised Pipeline Integration

var result = SupervisedExperiment
    .For(X, y)
    .WithGrid(new PipelineGrid()
        .AddModel<KNearestNeighbors>(g => g
            .Add("K", 3, 5, 7)
            .AddReducer<PCA>(r => r.Add("NComponents", 2, 5))
            .AddScaler<StandardScaler>(s => { }))
        .AddModel<DecisionTree>(g => g
            .Add("MaxDepth", 3, 5, 10)))
    .WithCrossValidator(CrossValidatorConfig.KFold(folds: 5))
    .Run();

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📌 Key Points

• Reducers are optional — existing pipelines work unchanged
• PCA uses the library's own EigenDecomposition — no external dependencies
• ExplainedVarianceRatio shows how much variance each component captures
• Grid search over NComponents finds the optimal dimensionality automatically
• Works with both supervised and clustering pipelines
• Follows the same FitTransform / Transform / Clone pattern as scalers
• Implements IHasHyperparameters for grid search integration